Re: Design of FIR filter with Sharp Transition and High Stop BandAttenuation

jim wrote:

  ...

I don't think you're really grasping the problem. What he has is a sampling array that has 4 times as many sample points as the output array. So the problem would seem to be a simple matter of devising a filter suitable for downsampling by 4. The kicker is that each of these four receptors aren't really measuring the same thing.
The conventional way of looking at it would be that each of the 4 receptors only 'sees' 1/4 of the signal (or some other division summing to unity) so you simply sum the outputs (or do weighted sum). Its like having 4 judges with different kind of color blindness voting to tell you what the grayscale brightness is. But there is probably more to it than that. For one thing his way of looking at it takes into account that the 4 receptors are not in the same location. Plus there is some overlap in the light frequencies that each receptor is sensitive to (note: that is a different sort of frequency than spatial frequency). So some sort of filtering could be better than simply naively adding the output of blocks of 4.

Another aspect of the problem is that the sensors being smaller than the cell size, the inherent filtering of blocky arrays is lost. There is a way to oversample the array that will make the filtering he wants possible, but I can't say it will help. First of all, when he says "halfband filter" he seems to mean the Nyquist rate for the pixel size. Before he can filter out those higher frequencies, he has to create them. (Is his "Y = (Mg+Ye) + (G+Cy) = (G+Cy)+ (Mg+Cy)..." right?)

I don't know enough about the structure of his sensor to suggest a scheme, but I think that creating phantom pixels is the right first step. For a stripe pattern of ... R1 G1 B1 R2 G2 B2 ... and assuming that the gains (weights) have already been adjusted, I would create grayscale pixels ... G1 B1 R2, B1 R2 G2, R2 G2 B2, ... so that each color stripe contributes to three pixels, then low-pass to 1/3 the phantom pixel rate. With details, we could probably work out a similar "oversampling" scheme for his line sensor.

This whole discussion hinges on what the sample rate really is. Maybe when it's all matrixed out, it really does boil down to an FIR running at the 4x rate, provided the signals are weighted beforehand. I don't know. I do know that FIRs can be flat enough and can have all the sharpness needed if latency isn't a problem. I don't see one scan line of latency being a problem for most uses, and that many taps would make a jim dandy filter if coefficient truncation doesn't mess it up too badly.

Jerry

Engineering is the art of making what you want from things you can get.
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